Finite Group DatabasebetaFinite Group Databasebeta| order | 22596 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×#11761640 |
| Fitting, socle, Hall | C3×C7×C269 ⋊ C4 |
| derived, Sylow | C269 ⋊ C3×C4×C7 |
| Hall | C7×C269 ⋊ C3×C4 |
| Hall | C3×C269 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #11761640 |
| commutator, hypocenter | C269 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C269 | C4 |
| prime radical | C3×C7×D269 | C2 |
| cosocle | D269 | C2×C3×C7 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C3×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5649 |
1491 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22596, 20);